Three students named Anderson are in the rolls of the Mordecai school.
Ann Anderson attended the school for a single term, the first part of 1811.
Mary F. Anderson attended the school for two terms, in 1818. She is listed as being from Richmond VA, and the name Henry Anderson is attached to her account.
William Anderson attended the school for two terms, in 1815. The name George Anderson is attached to his account.
William? Yes, boys attended the Mordecai school--they made up about 10% of the students ever enrolled. They were generally younger local boys who seem to have filled seats during low-enrollment years. So William Anderson was likely a Warrenton child who took classes at the school but lived at home. There were certainly families named Anderson in Warrenton at the time, but it's a common name and that's true of many towns in the 1810s, I suspect. Because of this, there isn't much more to find about these three students online--or, perhaps there is, but the few details I have here don't help me much in finding more.